Holographic Beta functions for the Generalized Sine Gordon Theory

TL;DR

This paper extends the Sine Gordon model with multiple cosine terms, computes its beta functions using both boundary RG techniques and holographic duality, and finds consistent results across methods.

Contribution

It introduces a generalized Sine Gordon theory with multiple cosine interactions and computes its beta functions via boundary and holographic methods, confirming their agreement.

Findings

Beta functions computed using boundary RG techniques.

Holographic calculations of beta functions agree with boundary results.

Field strength renormalization beta functions match previous studies.

Abstract

The Sine Gordon theory is generalized to include several cosine terms. This is similar to the world sheet description of a string propagating in a tachyon background. This model is studied as a (boundary) 2d euclidean field theory and also using an $AdS_3$ holographic bulk dual. The beta functions for the cosine vertex of this modified theory are first computed in the boundary using techniques based on the exact RG. The beta functions are also computed holographically using position space and momentum space techniques. The results are in agreement with each other and with earlier computations. The beta functions of the field strength renormalization are computed in position space. They match with the earlier results in \cite{Oak:2017trw}.